Institute of Linguistics, Shanghai Normal University, Shanghai 200234, China.
Proc Natl Acad Sci U S A. 2013 Jun 11;110(24):9698-703. doi: 10.1073/pnas.1303108110. Epub 2013 May 28.
It is generally difficult to define reasonable parameters and interpret their values in mathematical models of social phenomena. Rather than directly fitting abstract parameters against empirical data, we should define some concrete parameters to denote the sociocultural factors relevant for particular phenomena, and compute the values of these parameters based upon the corresponding empirical data. Taking the example of modeling studies of language competition, we propose a language diffusion principle and two language inheritance principles to compute two critical parameters, namely the impacts and inheritance rates of competing languages, in our language competition model derived from the Lotka-Volterra competition model in evolutionary biology. These principles assign explicit sociolinguistic meanings to those parameters and calculate their values from the relevant data of population censuses and language surveys. Using four examples of language competition, we illustrate that our language competition model with thus-estimated parameter values can reliably replicate and predict the dynamics of language competition, and it is especially useful in cases lacking direct competition data.
通常来说，在社会现象的数学模型中定义合理的参数并解释其数值具有一定难度。我们不应直接将抽象参数拟合到经验数据上，而应定义一些具体参数来表示与特定现象相关的社会文化因素，并根据相应的经验数据计算这些参数的值。以语言竞争的建模研究为例，我们提出了语言扩散原则和两种语言继承原则，用以计算我们从进化生物学中的洛特卡-沃尔泰拉竞争模型推导出的语言竞争模型中的两个关键参数，即竞争语言的影响和继承率。这些原则为这些参数赋予了明确的社会语言学意义，并根据人口普查和语言调查的相关数据计算了它们的值。通过四个语言竞争的例子，我们说明了使用这种方法估计参数值的语言竞争模型可以可靠地再现和预测语言竞争的动态，并且在缺乏直接竞争数据的情况下尤其有用。
